Exposure tools are used in photolithography to define patterns on objects such as integrated circuits. Exposure tools, however, may introduce errors that cause the resulting pattern defined on the object to differ from the intended pattern. For example, an astigmatism of a projection lens of an exposure tool may cause the resulting pattern to differ from the intended pattern. Known techniques characterize an exposure tool by describing the errors introduced by the exposure tool in order to compensate for these errors. Known techniques for characterizing an exposure tool, however, are typically inefficient and can be inaccurate. Consequently, known techniques for characterizing an exposure tool may be unsatisfactory in certain situations.